Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is obtuse.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
4.2 + 6.4 > 7.6
6.4 + 7.6 > 4.2
7.6 + 4.2 > 2.6
Hence, these set of numbers can be the measures of the sides of a triangle.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]a^{2} + b^{2} < c^{2}[/tex]
obtuse if [tex]a^{2} + b^{2} > c^{2}[/tex]
right if [tex]a^{2} + b^{2} = c^{2}[/tex]
∴The longest side is 7.6.
Hence, a = 4.2, b = 6.4 and c = 7.6;
Consider [tex]a^{2} + b^{2}[/tex] :
= [tex]4.2^{2} + 6.4^{2}[/tex]
= 58.6.
Now consider [tex]c^{2}[/tex] :
= [tex]7.6^{2}[/tex]
=57.76.
Thus, [tex]a^{2} + b^{2} > c^{2}[/tex]
Hence, the triangle is obtuse.
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Find two consecutiver odd intergers such that the sum of the smaller and 3 times the larger is 330
How do i do this???
Answer:
Step-by-step explanation:
Givens
Smallest odd number = 2x + 1 The one guarantees that the number is odd. The 2 in front of the x makes sure it is even to start with.
The larger odd number is 2x + 3.
Equation
2x + 1 + 3(2x + 3) = 330 Remove the Brackets
2x + 1 + 6x + 9 = 330 Combine
8x + 10 = 330 Subtract 10 from both sides.
8x +10-10 = 330 - 10 Combine
8x= 320 Divide both sides by 8
x = 40
Answer
2x + 1 = 2*40 + 1 = 81
2x + 3 = 2*40 + 3 = 83
Using the change of base formula, what is the solution of log₅x = log₃20 ? Round the answer to the nearest tenth.
Solution of log₅x = log₃20 is , x = [tex]5^{log_3(20)}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax =N[/tex]
where, a is the base of function or equation
x define expression
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c (a) +log_c (b) = log (a b)log a/b = log a - log blog a^x = x log alog a^a = 1What is change of base formula ?Change of base formula generally use to change the logarithm base to another base.
The formula for base change is :
[tex]log_bx = \frac{log_cx}{log_cb}[/tex]
where, c is the new base.
In the given question,
log₅x = log₃20
using base change this can be written as :
[tex]\frac{log_{10}x}{log_{10}5} = \frac{log_{10}20}{log_{10}3} \\\\= > log_{10}(x) = \frac{log_{10}20 . log_{10}5}{log_{10}3}\\ \\= > x = 5^{log_320}[/tex]
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Could someone please help me with algebra 1
Answer:
Step-by-step explanation:
yes I will
Are you not doing school today
What is the slope of a line that is parallel to the line y =-1/5 ?
0
5
undefined
Answer: 0
Step-by-step explanation:
The slope of the line y = -1/5 is zero because it is a horizontal line.
Parallel lines have the same slope, so the answer is also 0.
Solve the literal equation 4y-5x=-6 for y.
Answer:
First, take -5x then turn -5 to a positive 5 like so and add it to -6. So, -6+5= -1, so then take -1 + 4 which will equal 4 which is y.
Y=4
Solution of the literal equation 4y-5x=-6 for y is y = (5/4)x - (3/2).
What is literal equation?A literal equation are equations which have two or more unknown variables in them. A literal equation can be solved by adding or subtracting or multiplying or divide by same numbers on both sides of the equation in order to get an expression for the required variable.
Given an literal equation 4y - 5x = -6
We need to solve this equation for y , means separate y and make its coefficient 1
4y-5x =-6
Adding 5x both sides ⇒ 4y-5x+5x = -6 +5x
⇒ 4y = 5x-6
Divide both sides by 4 , we get
⇒4y/4 = (5x-6)/4
⇒ y = (5/4)x - (6/4)
⇒ y = (5/4)x - (3/2)
∴The solution for the variable y from the given literal equation 4y-5x=-6 is y = (5/4)x - (3/2)
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Solve each system by elimination or substitution.
y - 3= x , 4x + y = - 2
Using substitution method, the solution of the given system of equations is (-1, 2)
A system of equation can be solved using:
graphical methodsubstitution methodelimination methodThe given system of equations:
y - 3 = x ............ (1)
4x + y = -2 .............. (2)
To use substitution method, we need to isolate y in equation (1). Add 3 to both sides:
y - 3 + 3 = x + 3
y = x + 3 ............... (3)
Substitute y = x + 3 into equation (2):
4x + y = -2
4x + x + 3 = -2
5x + 3 = -2
5x = -5
x = -1
Substitute back x = -1 into equation (3)
y = x + 3
= -1 + 3 = 2
Hence, the solution is (-1, 2)
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What is the next fraction in this sequence?
1/2, 4/7, 9/14, 5/7,.....
The next fraction in this sequence is 11/14
Given data
1/2, 4/7, 9/14, 5/7,.....
How to find the next umber in the sequenceThe sequence is an arithmetic sequence and the terms are gotten by successive addition of the common difference
first term + difference = 2nd term
1/2 + d = 4/7
d = 4/7 - 1/2
d = 1/14
finding the fifth term
4th term + difference = 5th term
5/7 + 1/14 = 5th term
5th term = 11/14
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The Loft Theater has a center seating section with 3c + 8 rows and 4c - 1 seats in each row . Write an expression for the total number of seats in the center section .
The expression for the total number of seats in the center section is 12c² +29c - 8
Writing an expressionFrom the question, we are to determine the expression for the total number of seats in the center section
From the given information,
The theater has a center seating section with 3c + 8 rows and 4c - 1 seats in each row
The number of seats in the center section is the product of 3c + 8 and 4c - 1
Thus,
Number of seats in the center section = (3c + 8)(4c -1)
Number of seats in the center section = 12c² - 3c + 32c - 8
Number of seats in the center section = 12c² +29c - 8
Hence, the expression for the total number of seats in the center section is 12c² +29c - 8
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In ΔRST, \text{m}\angle R = (x+17)^{\circ}m∠R=(x+17) ∘ , \text{m}\angle S = (2x-2)^{\circ}m∠S=(2x−2) ∘ , and \text{m}\angle T = (5x+5)^{\circ}m∠T=(5x+5) ∘ . Find \text{m}\angle S.m∠S.
After calculating the value of x in the all angle sum equation of ΔRST, we have come to find that m∠S = 38°.
What is an angle in geometry?An angle is a figure generated by two rays or lines that have a common terminal in Plane Geometry. The term "angle" is derived from the Latin word "angulus," which meaning "corner." The two rays are known as the sides of an angle, while the common terminus is known as the vertex.
The plane angle does not have to be in Euclidean space. Dihedral angles are created by the intersection of two planes in Euclidean or other space. An angle is identified by the symbol "∠". The angle measurement between the two beams can be represented by the Greek letter θ,α, β etc.
We have given that
m∠R = (x+17)°
m∠S = (2x−2)°
m∠T = (5x+5)°
We know all the angles of a triangle add upto 180°
m∠R + m∠S + m∠T = 180°
(x+17)° + (2x−2)° + (5x+5)° =180°
8x + 20 = 180°
8x = 160°
x = 160°/8
x = 20°
And therefore, m∠S = (2(20)−2)°
= (40 - 2)°
= 38°
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Select the correct answer.
CAMERY
Which expression is equivalent to the given expression?
2x214x + 24
OA. 2(x-8)(x + 3)
OB.
(2x12)(x - 2)
OC. 2(x - 3)(x - 4)
OD. 2(x - 5)(x - 2)
Use the spinner to find the probability.
b. P(pointer not landing on green)
The probability of spinner pointer not landing on green is equal to 2/3 .
As given in the question,
Total colors in the spinner is equal to 6
Each color is 2 times
Total number of colored region =6
Number of green region = 2
Probability of pointer landing on green color region denoted by P(G)
Probability is
=(Total number of favourable outcomes) / (Total number of outcomes )
⇒P(G)=2/6
⇒P(G) =1/3
Probability of pointer not landing on green P(G') =1-P(G)
=1-(1/3)
=2/3
Therefore, the probability of spinner pointer not landing on green is equal to 2/3.
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According to a college survey, 22% of all students work full time. If 12 college students are randomly selected, find the probability that exactly three of them work full time.
The probability that exactly three of them work full time is 0.25.
How to calculate the probability?It should be noted that from the information, we want to find P(X = 3).
This will be illustrated as:.
12C3(1 - 22%)^9(0.22)³
= 220(0.78)^9(0.22)³
= 0.250
Therefore, the probability that exactly three of them work full time is 0.25.
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Express each fraction as a decimal to the nearest hundredth. 11/78
The nearest hundredth decimal of 11 / 78 = 0.14
11/78 = 0.14102564102564102564102564102564
The nearest hundredth decimal of 11 / 78 = 0.14
A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of a numerator, displayed above a line (or before a slash like 1⁄2), and a non-zero denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
In positive common fractions, the numerator and denominator are natural numbers. The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. The denominator cannot be zero, because zero parts can never make up a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates 3/4 of a cake.
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Solve each system.
7x + 2y = -8 , 8y = 4x
After solving each system, 7x + 2y = -8, 8y = 4x , the values of x and y are calculated to be -1 and -1/2 respectively.
The given equations, 7x + 2y = -8, and 8y = 4x, are considered to be linear equations as the highest power of the variables in these equations is one.
By rearranging the second equation, the value of x can be found to be,
8y = 4x
x = 8y / 4
x = 2y
Putting the calculated value of x in the second equation,
7x + 2y = -8
7(2y) + 2y = -8
14y + 2y = -8
16y = -8
y = -8/16
y = -1/2
To solve for x, put the calculated value of y in the first equation,
7x + 2y = -8
7x + 2(-1/2) = -8
7x - 1 = -8
7x = -8 + 1
7x = -7
x = -7/7
x = -1
Thus the values of x and y in these systems are calculated to be -1 and -1/2 respectively.
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The width of a rectangle is 8 units less than the length. The area of a rectangle is 9 units. What is the length, in units of the rectangle?
Answer:
The length would have to be 9, and the width 1
Step-by-step explanation:
l*W 9*1=9
Simplify the expression 9x-4-12x-3
Answer:
-3x - 7 is the answer
Step-by-step explanation:
your welcome
===================================================
[tex]9x-4-12x-3\\\\\\9x-12x-4-3\\\\\\-3x-7[/tex]<--------- SOLUTION=====================================================
#CarryOnLearning
[tex]\textcopyright ELIZA[/tex]
Which system of inequalities is represented by this graph?
A) { y≤2x−3 / y x+1
C) { y≤3x−2 / y x+1
you only have two answer choices but out off the two answer A is most correct.
100 POINTS + BRAINLEIST PLS ANWER ASAP
C is the correct answer:)
I need some help on this, how can I found the single power for this?
I need some help on this, how can I found the single power for this?
1) [tex](-5^{5})^{2}= 9765625[/tex]
2) [tex]\frac{12^{5} \times12^{7} }{-12^{4} } =-429981696[/tex]
Power is
An expression known as "power" denotes the process of repeatedly multiplying a value or integer.[tex]a^{n}[/tex] is often a power where n is the exponent and a is the base.
The amount of times a number has been multiplied by itself is shown by its exponent.
1) Given
[tex](-5^{5})^{2}\\\\[/tex]
Step1: [tex](-5^{5})=-3125[/tex]
Step2:[tex](-5^{5})^{2}=(-3125))^{2}=9765625[/tex]
This is how we will solve the power of [tex](-5^{5})^{2}\\\\[/tex]
2)Given
[tex]\frac{12^{5} \times12^{7} }{-12^{4} }[/tex]
Step1: [tex]12^{5} =248832[/tex]
Step2:[tex]12^{7} =35831808[/tex]
Step3:[tex]-12^{4} =-20736\\[/tex]
Step4: [tex]\frac{12^{5} \times12^{7} }{-12^{4} }=\frac{248831\times35831808}{-20736}[/tex]
Step5: [tex]\frac{12^{5} \times12^{7} }{-12^{4} } =-429981696[/tex]
This is how we will solve the power of [tex]\frac{12^{5} \times12^{7} }{-12^{4} }\\[/tex].
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what value could be added to 2/15 to make it greater than 1/2
Answer:
[tex] \frac{1}{2} - \frac{2}{15} = \frac{15 - 4}{30} = \frac{11}{30} \\ \\ we \: \: have \: \: to \: \: add \: \: any \: number \: \: which \: \: \\ is \: greater \: \: than \: \frac{11}{30} [/tex]
what is the average rate of change, please simply your answer (PICTURE BELOW)
Answer:
The answer to this question is 0
Step-by-step explanation:
see attached photo for explanation
I need this answered please
Answer:
2g+12 = Goran's height
When rocket approaches the moon engineers needed to plan how the lunar
Answer:
G would equal x because she is a guy and needs to poop
Step-by-step explanation:
Guadalupe spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -5.4°F. Between 9am and noon, the temperature rose 9.4°F. Between noon and 3pm, the temperature went down 13.6°F. Between 3pm and 6pm, the temperature went down 16.9°F. What was the temperature at 6pm?
The final temperature of a winter day at 6 pm will be negative 26.5°Ferenhiet.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
For science class, Guadalupe works on a winter day taking the temperature once every three hours. The temperature was -5.4°F at 9 a.m. The temperature increased by 9.4°F from nine till noon. The temperature dropped 13.6°F between noon and three o'clock. The temperature dropped 16.9°F between 3 and 6 o'clock.
Then the temperature at 6 pm will be
⇒ - 5.4°F + 9.4°F - 13.6°F - 16.9°F
⇒ - 35.9°F + 9.4°F
⇒ - 26.5°F
The temperature at 6 pm will be negative 26.5°F.
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find 2 numbers if their ratio is 9:11 and their difference is 6
Answer:
27:33
Step-by-step explanation:
turn the ratio into an equation by and add 6 to 9x to mae it equal to 11x and solve for x
Find the equation of the line that has a slope of
-5 and passes through the point (8,-6).
Write the equation in point-slope form.
Answer:
point slope form: y - y1 = m (x - x1), where m is slope and x1, y1 is a point the line passes through
here the slope m = 5, and the point x1,y1 = -3,6, so substituting the equation is:
y-6 = 5(x+3)
Step-by-step explanation:
Solve the formula for the height of the figure.
A=1/2bh
h=_
Use the formula to find the height.
h=_mm
4x=2x-12 ayudaaaaaaaaaaaaaaaaaaaa
Answer:
x = -6⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
What is 3 5/6×3????????????
Answer: 17.5
Step-by-step explanation: If the question is (35/6) * 3. Then it is 17.5
[tex]\frac{35}{6}*\frac{3}{1} = \frac{105}{6} = \frac{35}{2}[/tex]
which is 17.5 in decimal form
Answer:
11 1/2
Step-by-step explanation:
3 5/6x 3
multiply 3 by the denominator then add 5
so 3x6=18/6+5/6= 23/6 x 3
so 23/6 x 3/1 = 69/6
simplify 69/6 = 11 3/6 or 11 1/2
express 45(1)/(2)in simplest radical form
The given expression written in the simplest radical form is 3√5
Writing an expression in radical formFrom the question, we are to write the given expression in the simplest radical form
The given expression is 45^(1/2)
From one of the laws of indices, we have that
[tex]x^{y/n} = \sqrt[n]{x^{y} }[/tex]
Thus,
Applying this rule, the given expression can be written as
√45
Now, we will express the given radical expression in the simplest radical form
Expressing in simplest radical form
√45
= √(9 × 5)
= √9 × √5
= 3 × √5
= 3√5
Hence, the given expression written in the simplest radical form is 3√5
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